Fourth-Generation (4G) communication systems, such as LTE networks, use closed-loop beamforming techniques to improve throughput. In these systems, a receiver feeds back, among other things, precoding information, to a transmitter that recommends a precoder for use in transmitting beamformed signals back to the receiver. Since the selection of precoders is limited to particular codebooks, the recommended precoder may not be ideal based on the current channel conditions. MU-MIMO transmissions are particularly sensitive to this problem for a given codebook. Although errors from this problem may be reduced through the use of a larger codebook, recommending a precoder associated with a larger codebook would require significant additional feedback as well as defining a larger codebook. Additionally, the time and resources required to generate a PMI may be burdensome.
Thus, what are needed are systems and methods for precoding that reduce error without the use of a larger codebook. What are also needed are systems and methods for precoding that reduce channel state information (CSI) quantization error suitable for MU-MIMO in LTE networks. Further, an efficient way of generating a PMI quickly and with affordable use of resources is also needed.